Remark 2 
Note that the coordinate-wise separability property is not shared among other related algorithms in the literature.
For instance, the choice \(\psi = \frac{1}{2} \left\Vert \cdot  \right\Vert _q^2\)  for \(1/p + 1/q = 1\) , which is referred to as the \(p\) -norm algorithm [1]}, [2]} is not fully coordinate-wise separable since it requires computing \(\left\Vert w_t \right\Vert _p\)  at each step (see, e.g., [2]}).
Another related algorithm is steepest descent, where the Bregman divergence in REF  is replaced with \(\left\Vert \cdot  \right\Vert ^2\)  for general norm \(\left\Vert \cdot  \right\Vert \) .It is also worth noting that steepest descent is not an instance of mirror descent since \(\left\Vert \cdot  \right\Vert ^2\)  is not a Bregman divergence for a general norm \(\left\Vert \cdot  \right\Vert \) .
However, for similar reasons, the update rule is not fully separable.

